HγC W1: From τ to Emergent Effective Time in the HγC Framework

This paper investigates the conditions under which an effective macroscopic time parameter can emerge within the HγC framework from a microscopic substrate organized only by pre-temporal relational update ordering. The microscopic update parameter τ is treated not as physical time, but as an ordering parameter for successive local relational state transitions. The paper argues that temporal directionality arises prior to clock-like time through irreversible accumulation of retained relational traces and the resulting asymmetry in admissible future transitions. On this basis, W1 identifies the regime conditions under which a continuous effective time variable teff becomes meaningful after coarse-graining.…